STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

Is extended biopsy protocol justified in all patients with PSA≥20ng/mL?

The aim of this study was to investigate whether it was necessary to increase the number of cores at initial prostate biopsy with patients of prostate-specific antigen （PSA） ≥ 20 ng/mL and to explore an appropriate individualized transrectal ultrasonograhpy （TRUS）-guided prostate biopsy for the detection of prostate cancer in men suspicious of prostate cancer. Methods： A total of 115 patients with PSA ≥ 20 ng/mL and suspicious of prostate cancer were prospectively randomized to perform TRUS-guided biopsy. Patients were randomized to a ＂6 ＋ X＂ cores or a ＂10 ＋ X＂ cores protocol. The primary end point was cancer detection rate. Secondary end points were cancer characteristics, rate of complications and the level of pain experienced by patients during TRUS-guided prostate biopsy. Results： Preoperative variables were similar in both groups. The overall prostate cancer detection rate was 73.9%. The ＂10 ＋ X＂ cores strategy increased cancer detection rate only 9.7% in patients with PSA ≥ 20 ng/mL but 〈 50 ng/mL, while there was no difference between the two strategies for cancer detection in patients with PSA ≥ 50.1 ng/mL. The number of extended biopsy cores and pain score of extended biopsy in prostate cancer patients increased significantly （P 〈 0.001）. Conclusion： Our findings suggest that there is no significant advantage in using extended biopsy protocol in all patients with PSA≥20 ng/mL.

Optimizing prostate biopsy for repeat transrectal prostate biopsies patients

Objective： Diagnosis of patients with negative prostate biopsy and persistent suspicion of prostate cancer re- mains a serious problem. In this study, we investigated the application of optimizing prostate biopsy for patients who need repeat prostate biopsy. Methods： In this prospective, non-randomized phase-I clinical trial, the prostate cancer detection rate of initial detection scheme was compared with optimizing prostate biopsy scheme. The number of punctures of initial detection scheme was the same as that of optimizing prostate biopsy scheme. The puncture direction of optimizing prostate biopsy was a 45~ angle to the sagittal plane from front, middle, and back. The two cores from each lateral lobe were horizontally inwardly inclined 45~. Results： A total of 45 patients with initial negative biopsy for cancer were received the optimizing prostate biopsy scheme. The cancer detection rate was 17.8% （8/45）, and prostate intraepithelial neoplasm （PIN） was 6.7% （3/45）. The pa- tients receiving repeat transrectal prostate biopsies were pathologically diagnosed as lower Gleason grade prostate cancers. Conclusion： The cancer detection rate of repeat biopsy prostate cancer is lower than that of initial biopsy. Our study showed that the optimizing prostate biopsy is important to improve the detection rate of repeat transrecta~ prostate biopsies patients.